Approach to the construction of the spaces $ S{D^p}[\mathbb{R}^\infty]$ for $1 \leq p \leq \infty$

Abstract: The objective of this paper is to construct separable Banach spaces $S{D^p}[\mathbb{R}^\infty]$ for $1\leq p \leq \infty$, each of which contains the $L^p[\mathbb{R}^\infty] $ spaces, as well as finitely additive measures, as compact dense embedding. Also these spaces contains Henstock-Kurzweil integrable functions.